Conditional Reasoning Exercises

To do well on the LSAT (especially the Logic Games) it is very important to become comfortable working with conditional reasoning. For example, when given the rule “If A then B” you must know what must be true given that rule, and you must also know what doesn’t have to be true on the basis of the rule. You must also be able to link conditional statements together to form a single (sometimes long) chain of conditional statements. In the following exercises you should diagram the rule(s), forming a single chain, and then answer the questions asking what must be true given the rules.

Exercises

The exercises refer to the following cats that are available for adoption at the local shelter: Alvin, Billie, Cinder, Django, Ella, Frank, and Gary.

1. If Billie is adopted, then Frank must be adopted as well.

If Frank is not adopted, what else must be true?

2. If Billie is adopted, then Frank is not adopted.

If Frank is adopted, what else must be true?

3. If Billie is not adopted, then Frank is adopted.

If Frank is not adopted, what else must be true?

4. If Billie is not adopted, then Frank is not adopted.

If Frank is adopted, what else must be true?
If Billie is adopted, what else must be true?

5. If Billie is adopted, then Frank is adopted. If Frank is adopted then Gary is not adopted.

If Gary is adopted, what else must be true?

6. If Billie is adopted, then Frank is not adopted. If Frank is not adopted then Gary is adopted.

If Gary is not adopted, what else must be true?

7. If Billie is not adopted, then Frank is adopted. If Gary is adopted, then Frank is not adopted.

If Billie is adopted, what else must be true?
If Billie is not adopted, what else must be true?

8. If Billie is adopted, then Frank is not adopted. If Gary is adopted, then Frank is adopted.

If Gary is adopted, what else must be true?
If Gary is not adopted, what else must be true?

9. If Alvin is adopted, then Frank is not adopted. If Frank is not adopted, then Gary is not adopted. If Gary is not adopted, then Ella is adopted.

If Ella is not adopted, what else must be true?
If Alvin is not adopted, what else must be true?

10. If Alvin is not adopted, then Frank is adopted. If Frank is adopted, then Cinder is adopted. If Gary is adopted, then Cinder is not adopted.

If Gary is adopted, what else must be true?
If Gary is not adopted, what else must be true?

11. If Alvin is adopted, then Billie is adopted. If Frank is adopted, then Billie is not adopted. If Frank is not adopted, then Gary is not adopted. If Gary is not adopted, then Ella is adopted.

If Ella is not adopted, what else must be true?
If Gary is not adopted, what else must be true?

12. If Django is adopted, then Billie and Frank are not adopted. If Billie is not adopted, then Gary is adopted.

If Gary is not adopted, what else must be true?
If Frank is not adopted, what elsemust be true?

13. If Cinder is not adopted, then either Gary or Frank are adopted. If Frank is adopted then Django is not adopted.

If Django is adopted, what else must be true?
If Gary is not adopted, what else must be true?
If neither Gary nor Frank are adopted, what else must be true?

14. If Gary is adopted, then either Frank or Cinder are not adopted. If Frank is not adopted, then Django is adopted.

If Django is not adopted, what else must be true?
If Frank is adopted, what else must be true?
If Gary is not adopted, what else must be true?

15. If Alvin is adopted, then either Gary or Frank are adopted. If Gary or Frank are adopted, then Ella is not adopted. If Cinder is not adopted, then Ella is adopted.

If Cinder is not adopted, what else must be true?
If Gary is adopted, what else must be true?

16. If Alvin is adopted, then both Billie and Cinder are adopted. If Billie is adopted, then Django is not adopted. If Cinder is adopted, then Ella is adopted. If Django is not adopted, then Frank is not adopted. If Ella is adopted, then Gary is adopted.

If Gary is not adopted, what else must be true?
If Frank is adopted, what else must be true?
If Billie is adopted, what else must be true?

17. If Alvin is adopted, Billie is not adopted. If Frank is adopted then Billie is adopted. If Frank is not adopted, then either Gary or Ella are adopted. If Gary is adopted, then Cinder is adopted. If Ella is adopted, then Django is not adopted.

If Django is adopted, what else must be true?
If Frank is not adopted, what else must be true?
If neither Gary nor Ella are adopted, what else must be true?

Solutions

The exercises refer to the following cats that are available for adoption at the local shelter: Alvin, Billie, Cinder, Django, Ella, Frank, and Gary. Solutions are in blue.

1. If Billie is adopted, then Frank must be adopted as well.

If Frank is not adopted, what else must be true? Billie is not adopted.

2. If Billie is adopted, then Frank is not adopted.

If Frank is adopted, what else must be true? Billie is not adopted.

3. If Billie is not adopted, then Frank is adopted.

If Frank is not adopted, what else must be true? Billie is adopted.

4. If Billie is not adopted, then Frank is not adopted.

If Frank is adopted, what else must be true? Billie is adopted.
If Billie is adopted, what else must be true? Nothing

5. If Billie is adopted, then Frank is adopted. If Frank is adopted then Gary is not adopted.

If Gary is adopted, what else must be true? Frank is not adopted and Bille is not adopted.

6. If Billie is adopted, then Frank is not adopted. If Frank is not adopted then Gary is adopted.

If Gary is not adopted, what else must be true? Frank is adopted and Billie is not adopted.

7. If Billie is not adopted, then Frank is adopted. If Gary is adopted, then Frank is not adopted.

If Billie is adopted, what else must be true? Nothing.
If Billie is not adopted, what else must be true? Frank is adopted and Gary is not adopted.

8. If Billie is adopted, then Frank is not adopted. If Gary is adopted, then Frank is adopted.

If Gary is adopted, what else must be true? Frank is adopted and Billie is not adopted.
If Gary is not adopted, what else must be true? Nothing.

9. If Alvin is adopted, then Frank is not adopted. If Frank is not adopted, then Gary is not adopted. If Gary is not adopted, then Ella is adopted.

If Ella is not adopted, what else must be true? Gary and Frank are adopted and Alvin is not.
If Alvin is not adopted, what else must be true? Nothing.

10. If Alvin is not adopted, then Frank is adopted. If Frank is adopted, then Cinder is adopted. If Gary is adopted, then Cinder is not adopted.

If Gary is adopted, what else must be true? Cinder and Frank are not adopted and Alvin is adopted.
If Gary is not adopted, what else must be true? Nothing.

11. If Alvin is adopted, then Billie is adopted. If Frank is adopted, then Billie is not adopted. If Frank is not adopted, then Gary is not adopted. If Gary is not adopted, then Ella is adopted.

If Ella is not adopted, what else must be true? Gary and Frank are adopted. Billie and Alvin are not.
If Gary is not adopted, what else must be true? Ella is adopted.

12. If Django is adopted, then Billie and Frank are not adopted. If Billie is not adopted, then Gary is adopted.

If Gary is not adopted, what else must be true? Billie is adopted and Django is not.
If Frank is not adopted, what else must be true? Nothing.

13. If Cinder is not adopted, then either Gary or Frank are adopted. If Frank is adopted then Django is not adopted.

If Django is adopted, what else must be true? Frank is not adopted.
If Gary is not adopted, what else must be true? Nothing.
If neither Gary nor Frank are adopted, what else must be true? Cinder is adopted.

14. If Gary is adopted, then either Frank or Cinder are not adopted. If Frank is not adopted, then Django is adopted.

If Django is not adopted, what else must be true? Frank is adopted.
If Frank is adopted, what else must be true? Nothing.
If Gary is not adopted, what else must be true? Nothing.

15. If Alvin is adopted, then either Gary or Frank are adopted. If Gary or Frank are adopted, then Ella is not adopted. If Cinder is not adopted, then Ella is adopted.

If Cinder is not adopted, what else must be true? Ella is adopted, and Gary, Frank, and Alvin are not.
If Gary is adopted, what else must be true? Cinder is adopted and Ella is not.

16. If Alvin is adopted, then both Billie and Cinder are adopted. If Billie is adopted, then Django is not adopted. If Cinder is adopted, then Ella is adopted. If Django is not adopted, then Frank is not adopted. If Ella is adopted, then Gary is adopted.

If Gary is not adopted, what else must be true? Ella, Cinder, and Alvin are not adopted.
If Frank is adopted, what else must be true? Django is adopted and Billie and Alvin are not.
If Billie is adopted, what else must be true? Django and Frank are not.

17. If Alvin is adopted, Billie is not adopted. If Frank is adopted then Billie is adopted. If Frank is not adopted, then either Gary or Ella are adopted. If Gary is adopted, then Cinder is adopted. If Ella is adopted, then Django is not adopted.

If Django is adopted, what else must be true? Ella is not adopted.
If Frank is not adopted, what else must be true? Either Gary or Ella is adopted.
If neither Gary nor Ella are adopted, what else must be true? Frank and Billie are adopted and Alvin is not.